Admission rates for super-selective colleges are headed in one direction: Down. Stanford, with the most competitive admissions in the country, this year edged below the 5 percent mark for the first time. Harvard’s rate, second-lowest among major colleges, hovers right above that threshold.

The admission rates are getting so low that a New York Times columnist joked that Stanford’s this year was 0 percent — with everyone denied access to the elite school; the truth is, if you apply to Stanford you probably won’t get in. It’s not quite at the vanishing point, but the real rate of 4.7 percent at the private university in Silicon Valley is still astonishing compared to a decade ago. For the class entering in fall 2006, Stanford admitted a share more than twice as large as this year (but still quite low): 10.9 percent.

The numbers game reflects the frenzy of competitive admissions. The more applications, the lower the rate, unless a college grows enrollment to match rising demand. Some colleges seem to do everything they can to boost applications, which enables them to deny more applicants, making the school look more selective.

But the most prestigious schools don’t have to gin up demand. Their rising application totals simply reflect the perennial national and global power of their brands. Stanford drew 43,997 applicants this year, up from 42,497 the year before. Harvard’s total was 39,041, up from 37,307. Cornell led the eight Ivy League schools (which don’t include Stanford) in number of applications, with 44,966, up from 41,900.

A quick scan of official news releases and student newspaper reports found lower admission rates this year at several prominent colleges and universities. The Washington Post is keeping track of admission rates at top schools for the incoming fall class, and for the previous year’s class. We will update the list as we gather more data from selective colleges. It is important to note that these figures combine all offers, from the early and regular phases of the cycle. “Early decision” applicants — who apply in the fall and commit to enroll if accepted — will often find the admission rate for their group is much higher than the total rate. Regular applicants typically apply in January, get offers by April 1 and then weigh their choices. They have until May 1 to decide where to enroll.

2016 College Admission RatesThe sortable table below includes selected top schools with data available as of April 1, but please check back, as the list will be updated. The admission rates for 2016 are preliminary; they may rise depending on the number of wait-listed students at a given school who are ultimately offered admission.